On a Regularity Theorem for Weak Solutions to Transmission Problems with Internal Lipschitz Boundaries
- 1 August 1992
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 115 (4) , 1069-1076
- https://doi.org/10.2307/2159357
Abstract
We show that if is a weak solution to <!-- MATH $\operatorname{div} (A\nabla u) = 0$ --> on an open set containing a Lipschitz domain , where <!-- MATH $A = kI{\chi _D} + I{\chi _{\Omega /D}}(k > 0,k \ne 1)$ --> 0,k \ne 1)$">. Then, the nontangential maximal function of the gradient of lies in <!-- MATH ${L^2}(\partial D)$ --> .
Keywords
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